Non-linear effects on supernova neutrino oscillations, associated with neutrino–neutrinointeractions, are known to induce collective flavor transformations near the supernova corefor . In scenarios with very shallow electron density profiles, these transformations havebeen shown to couple with ordinary matter effects, jointly producing spectraldistortions both in normal and in inverted hierarchy. In this work we consider acomplementary scenario, characterized by higher electron density, as indicated byshock-wave simulations during a few seconds after bounce. In this case, early collectiveflavor transitions are decoupled from later, ordinary matter effects. Moreover,such transitions become more amenable to both numerical computations andanalytical interpretations in inverted hierarchy, while they basically vanish innormal hierarchy. We numerically evolve the neutrino density matrix in the regionrelevant for self-interaction effects, using thermal spectra and a representative valuesin2θ13 = 10−4. In the approximation of averaged intersection angle between neutrino trajectories, oursimulations neatly show the collective phenomena of synchronization, bipolar oscillations,and spectral split, with analytically understandable features, as recently discussed in theliterature. In the more realistic (but computationally demanding) case of non-averagedneutrino trajectories, our simulations do not show new significant qualitative features,apart from the smearing of ‘fine structures’ such as bipolar nutations. Our results seem tosuggest that, at least for non-shallow matter density profiles, averaging over neutrinotrajectories plays a minor role in the final outcome. In this case, the swap ofνe andνμ,τ spectraabove a critical energy may represent an unmistakable signature of the inverted neutrino hierarchy, especiallyfor θ13 small enough to render further (ordinary or even turbulent) matter effects irrelevant.